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The possible existence of distinct regimes of barotropic circulation in closed annular channels at the same external parameters governing the flow dynamics is investigated both experimentally and numerically. Transitions between the regimes are realized by means of varying the value of the main parameter determining the velocity field energy (for example, the current controlling the Ampere force in the case of MHD generation of a velocity field) with subsequent reconstruction of the former parameter value. Depending on the channel rotation period or the configurations of magnet locations in the case of MHD generation or sources and sinks in numerical experiments the following results are possible. (1) The initial and final regimes differ quantitavely in the number of cyclonic or anticyclonic vortices generatted. (2) The number of vortex formations does not change but their localization in space, for example, the angular coordinates of their centers, varies. (3) After the change and reconstruction of the original value of the governing parameter the flow returns to the regime almost undistinguishable from the original regime. The flow patterns and the corresponding diagrams for laboratory experiments and numerical simulations based on shallow water equations are presented.

Mass exchange between the atmosphere of turbulent vortex ring and the surrounding medium is investigated in the initial stage of motion using the shadow visualization method. For this purpose, vortex rings in which the liquid has a different density as compared with the density of the surrounding medium are generated. The experiments are carried out for various values of the density differences, the velocities, and the vortex sizes. The characteristic time and space scales of mass exchange are determined. It is concluded that the basic mechanism of mass exchange is turbulent diffusion. The turbulent diffusion coefficient in the atmosphere of vortex ring is estimated using the characteristic time of mass exchange.

To predict the boundary layer transition on swept wings, experimental and numerical researches were conducted to obtained the accurate boundary layer transition front and to evaluate the performance of two transition predicting models. Flow visualization and temperature measurement over a 65° swept wing were carried out under M = 6 with nano-tracer-based planar laser scattering system and temperature sensitive paints. Meanwhile, the kT–kL–ω and γ–Reθt turbulence models were used to predict the boundary layer transition. Experiment results reflect that the transition front on the wing consists of three parts, including the transition near the wing root induced by separation, the transition dominated by stationary crossflow vortices and the transition in the connected region. The comparison between the simulation and experiment shows that the kT–kL–ω model performs better than γ–Reθt model in predicting the shape and position of the transition front, as well as the limiting streamlines. Thus, the kT–kL–ω model is more suitable in predicting the boundary layer transition for this type of swept wing.

A high-order discontinuous Galerkin method is employed to study the evolution of the flow structure in the gap and near wake of two tandem cylinders in the alternating in the gap (AG) regime. The transient characteristics of the flow, vorticity, and pressure fields, the transient circumferential pressure distribution, and the streamwise velocity along the centerline of the wake are studied under a Reynolds number of 200 and a pitch ratio of 2.3. The results show that the gap-flow occurs between the two tandem cylinders in the AG regime, and the gap-flow interacts with quasistatic vortices in the gap to cause unilateral or bilateral reattachment of the separated shear layer. In addition, under the influence of the gap-flow, a near-wake vortex is generated behind the downstream cylinder, which significantly affects the length of the recirculation bubble. Finally, the physical mechanism of reattachment of the shear layer and the generation of gap-flow in the AG regime are discussed.

Numerical simulations of incompressible laminar flow past a circular cylinder using wavy wall confinement are performed in order to study drag reduction and vortex shedding suppression for Reynolds numbers (50 ≤ Re ≤ 280) and blockage ratios (0.5 ≤ D/H ≤ 0.9), where D is the cylinder diameter and H is the channel height. The optimum configuration of wavy wall confinement is identified to have an amplitude of 0.2D and wavelength of 4D which manifests the minimum drag coefficient and complete vortex shedding suppression (zero lift coefficient). The flow over the cylinder with optimized wavy wall confinement produces a stable vortex pair in the wake of the cylinder. The length of vortex pair in the wake increases by increasing the Reynolds number and decreasing the blockage ratio. The drag on the cylinder reduces when the length of vortex pair increases due to early flow separation and reduction in pressure drag. The drag coefficient decreases by 36% in comparison to the plane wall confinement at D/H = 0.5. The drag coefficient decreases for wavy wall configuration by about 67% for D/H = 0.7 and 94% for D/H = 0.9. The lift coefficient remains zero at all Reynolds numbers and blockage ratios which indicates complete suppression of vortex shedding.

The flow around an staggered arrangement of seven cylinders is numerically studied using the finite element method to solve the two-dimensional and incompressible Navier—Stokes equations. The Reynolds number is 200 and the spacing ratios $$L{\text{/}}D$$ = 1.1–5. In accordance with different hydrodynamic characteristics and vortex street arrangements, three distinct forms of wake flow can be identified, namely, the single bluff-body pattern ( $$1.1 < L{\text{/}}D < 1.5$$ ), the deflected pattern ( $$1.5 < L{\text{/}}D$$ < 3), and the vortex impact pattern ( $$3 < L{\text{/}}D < 5$$ ). For the further in-depth study of the characteristics of different wake patterns, the variations of the hydrodynamic forces on seven cylinders and the underlying mechanisms are analyzed and the wake structures are presented. The results of the analysis show that the gap flow under different wake patterns has different effects on the change of the hydrodynamic characteristics. It is found that the change of the wake structure is closely related to the change of the wake pattern.

Wind tunnel experiments on the control of flow in a three-dimensional boundary layer are performed using a multidischarge actuator system. The boundary layer was produced on a swept plate with an induced streamwise negative pressure gradient. The actuator system used a near-surface barrier discharge for producing a unidirectional three-dimensional force action over a lengthy region of the plate surface. The possibility of considerably reducing the cross-flow velocity and mitigating the intensity of stationary vortices that produce the cross-flow instability by means of the action of an actuator system is confirmed.

The excitation of pressure fluctuations in a model jet-driven Helmholtz oscillator is experimentally investigated. An axisymmetric channel consisted of a cylindrical chamber with a nozzle in the front cover and an outlet opening in the back one. Optimal geometric dimensions of the chamber, nozzle, and outlet were chosen to achieve the greatest amplitude of the pressure fluctuations in the chamber. The nozzle length-to-diameter ratio ln/dn varied in the 0.77 ≤ ln/dn ≤ 4.17 range. The cylindrical chamber length Lch determining the air jet length ljet in the interval between the covers and Lch/dn = 0.5–3.5. The outlet opening diameter in the back cover dout varied within the limits dout/dn = 1–2.5. The optimal nozzle length ln/dn, the corresponding chamber length Lch/dn, and the outlet diameter dout/dn are determined. The air jet development within the nozzle and the formation of an inverse flow zone between the nozzle wall and the jet periphery and a chain of vortex structures in the mixing layer are considered. The generation of a jet tone of the opening on the frequency of the feedback in the jet and a family of acoustic modes on the resonance frequency with a smooth increase in the jet velocity from 0 to 70 m/s is studied.

The numerical solution of the problem of compressible gas flow past a plate with upstream-moving surface is obtained. Unstable time-periodic and stable steady-state solutions of this problem are discussed. A new type of unsteady periodic flow in which the varying characteristics turn out to be integrally asymmetric at transonic velocities is obtained.

The problem of evolution of an axisymmetric vortex generated by an infinitely elongated cylinder rotating around its axis in a compressible viscous fluid is considered. The asymptotic solution is constructed for large times. The conditions under which the velocity circulation at long distances is higher than in the incompressible fluid case are determined.

The paper considers stationary solutions for the motion problem of a finite layer of an incompressible polymer fluid over an infinite rotating disk. An approximate stationary solution representation is used, similar to the self-similar Karman solution for a viscous fluid. Examples of stationary numerical solutions are given for various values of the problem’s parameters.

In this paper, we study plane diffusion-vortex flows in the half-plane of a viscous incompressible fluid controlled by the boundary motion. At the boundary, either the longitudinal velocity or shear stress can be specified as functions of time. Classical self-similar solutions take place if these functions coincide with the Heaviside function. A linearized problem for relatively small initial perturbations superimposed on the kinematics in the entire half-plane is formulated. It consists of one biparabolic equation with variable coefficients with respect to the complex-valued current function and four homogeneous boundary conditions. Exponential estimates, which are estimates of the attenuation for some values of the parameters while they indicate the nature of the growth of perturbations for others, are derived using the method of integral relations. Some characteristic cases of specifying the boundary velocity or tangential stress on it are analyzed.

The results of the numerical investigation of supersonic flow past a sharp slender body at an angle of attack are given with reference to the example of an axisymmetric cylindrical body with a conical nose. Separated and vortex structures developed at various angles of attack are identified. The effect of anomalous increase in pressure on the leeward side is explained.

The statistical method for describing the intermittency coefficient in the region of laminar–turbulent boundary layer transition at the low level of external perturbations is proposed. The method is based on the assumption that turbulence develops when the velocity deviates locally in space and time from the mean by a threshold value. The analytical formulas are obtained for the frequency of occurrence of the coherent structures (turbulent spots and wedges) and for the intermittency coefficient or the mean fraction of the surface area covered by them in the case of two basic scenarios of transition, namely, the enhancement of steady crossflow instability vortices on the swept wing and the Tollmien–Schlichting waves.

An asymptotic method for investigating small oscillations of fluids in cylindrical tanks with longitudinal damping partitions is presented. The effect of the number and width of partitions on the hydrodynamic parameters and the damping coefficients of fluid oscillations is studied in detail for the case of a circular cylindrical enclosure with a plane bottom. The numerical results are obtained using the finite element method. Basing on the asymptotic theory of vortex resistance a perturbation method applicable for determining the fluid oscillation damping in tanks of arbitrary shape with partitions of small relative width is developed.

The structure and dynamics of flows near a horizontal and inclined plates in stratified and homogeneous fluids in a transient vortex regime are studied for various angles of inclination of the plate to the horizon and various geometrical modifications of its front and rear edges. This study is based on high-precision numerical modeling of the fundamental system of equations, which allows calculations of both stratified and homogeneous viscous liquids in a unified formulation. Instantaneous patterns of the vorticity fields, pressure gradient, and density, as well as the values of forces and moments acting on the surface of the plate are analyzed at different inclination angles, curvature radii of the front edge of the plate, and sharpness coefficients of the rear part. The pressure field consists of multi-scale spotted structures with a negative values of pressure, corresponding to the positions of vortical elements of the flow, whose spatial and time scales, geometric features, manifestation level, and dissipation rate essentially depend on the angle of inclination of the plate to the horizon, geometrical modification of its edges, and the type of the fluid. Special attention is paid to the fine structure of the flow near the front edge of the plate, which is the area with the most diverse scales of the flow, in which both large-scale and small-scale vertical structures form and actively interact.

When simulating incompressible flow around airfoil using vortex methods of computational hydrodynamics, it is necessary to solve the boundary integral equation with respect to the intensity of the vortex sheet at the airfoil surface line. For its approximate solution, the Galerkin method with a piecewise-constant and piecewise-linear representation of the solution on the airfoil surface line can be applied. The coefficients of the system of linear equations, arising from the procedure of discretization of the integral equation, e xpress the influence of the vortex sheet located on the panels of the airfoil surface line on other panels; the components of the right-hand side vector express the influence of point vortices that simulate a vortex wake in the flow domain. For the case of the airfoil surface line approximation with a polyline consisting of rectilinear panels, exact analytical expressions are obtained for the coefficients of the matrix and the right-hand side vector; for the case of taking into account the curvature of the panels, an approach for their approximate calculation is proposed and all the necessary formulae are derived.

This paper considers the steady and unsteady swirling axisymmetric flows of a homogeneous viscous incompressible fluid. The possibility of the existence of helical vortex lines on the surface of revolution homeomorphic to a torus is investigated. An example of unsteady flow in which there are helical vortex lines is given. It is proved that the existence of helical vortex lines lying on the surface of revolution homeomorphic to a torus is impossible in a steady axisymmetric flow of a viscous incompressible fluid.

The phenomenon of spontaneous rotation of melting ice on a solid substrate and on the surface of water has been confirmed by experiments in this work. The rotation velocity was found to increase with the temperature of the reservoir. Using the dying technique, a vortex flow was determined to appear directly under the ice block in experiments placing an ice block on the free surface of a resting liquid. A recorded vortex flow causes ice to rotate. The rotation parameters were measured, and the critical value of the depth of the resting fluid layer, necessary for the start of ice block rotation, was obtained.

The process of laminar-turbulent transition in a boundary layer is studied in terms of vortex evolution, from the growth of weak external disturbances to the formation of intense waves resulting in the development of a turbulent flow having internal scales of the problem. The self-sustained turbulence is obtained and the flow patterns on the plate surface and inside the turbulent boundary layer with fluid plumes propagating from the plate surface in the form of “bursting” are investigated. The basic flow parameters are calculated, such as the frequency and intensity of gas velocity fluctuations in turbulent spots. The validity of a local turbulence similarity law is confirmed. The study is performed on the basis of direct numerical simulation of a flow over a plate with Mach number M = 2 using unsteady Navier-Stokes equations without any closure model of turbulence.

—A new explicit form of the Navier—Stokes equations is obtained by means of the Reynoldsaveraging of these equations within the framework of the generally accepted model of spectrum-averaged fluctuations. The equations thus obtained contain some new terms caused by density fluctuations, while certain their terms included earlier on the intuitive level are now physically validated. The equations of the k—ω model are derived using the method of moments. A new equation for the vortex fluctuations, written earlier on the intuitive and analogue level, is obtained from the general momentum equation.

Elements of group analysis are given for a submodel of plane steady isentropic gas flows. The problem of group classification by arbitrary elements of the equation of state and the values of the Bernoulli and vortex integrals is solved. Optimal systems of subalgebras for two four-dimensional Lie algebras arising in the group classification are constructed. For some cases, the classification of invariant solutions by the optimal system is carried out. Physical interpretation of some solutions is given.

Periodic perturbations in the core of a thin isochronous vortex ring in an inviscid incompressible fluid are investigated in the linear approximation. The aim of the study is to construct the system of basic displacements, namely, the complete system of solutions of the Helmholtz equation for vorticity perturbations inside the core of a vortex ring with a given frequency in the form of expansion in the ring thinness parameter μ. The structure of basic displacements depends substantially on the fact to what extent the frequency of the forcing action is close to the resonance frequencies of the system. If the difference between these frequencies is small, then, in addition to the ring thinness μ, the second small parameters arises in the problem. This leads to significant complication of the procedure of obtaining the solution and appearance of considerable corrections in the subsequent approximations of the expansion procedure. The case of isochronous vortex ring in which the periods of revolution of liquid particles are identical is considered. Obtaining the threedimensional oscillations in such flows turns out to be the simplest since there are no perturbations of the continuous spectrum for the isochronous ring. The system of basic displacements is the necessary element in deriving the dispersion relation for the eigen-oscillations of the vortex ring. The solutions obtained can also serve as an instrument to analyze the reaction of flows with curvilinear vortex lines or flows localized in toroidal regions to the external excitation.

It is known that turbulence is characterized by intermittence which is closely related to the development of unsteady nonisotropic intense small-scale vortex structures. In this study, small fluid particles from the inertial range of isotropic turbulence are considered. It is shown that the phenomenon of rotation intensification and stretching of the particles can be analyzed theoretically. In recent experimental and numerical studies, where this phenomenon was called “the pirouette effect”, its significance in the mechanism of the intense small-scale structures generation was discussed. In this study, a linear stochastic Lagrangian model for the effect is developed. In this model, the kinetic equation for the distribution function of the squared cosine of the angle between the vorticity and the eigenvector of the strain rate tensor of a fluid particle is derived and time history asymptotics of this quantity are analytically calculated at large and small times. The results are in good agreement with the recent experiments and numerical calculations. An analysis made in this study shows that the linear processes probably play the crucial role in certain processes in the isotropic turbulence, which is known to be a principally nonlinear phenomenon. The model developed makes it possible to analyze the statistics of the Lagrangian dynamics of small fluid particles in the inertial range which can be useful in some computational approaches to turbulence.

Junction flows are subject to an intense adverse pressure gradient and three-dimensional separation when encountering a wall-mounted obstacle. A dynamically rich horseshoe vortex system is formed in this region. In this study the junction flow at the interaction of a wing and a flat plate is investigated. The numerical modelling is carried out using the three-dimensional large eddy simulation (LES) approach at the Reynolds number Re = 1.15×105 based on the wing’s maximum thickness T and the free stream velocity Uref. The comparison with the experimental results shows that the numerical simulations fairly accurately reproduce the phenomenon under study. The dynamic mode decomposition (DMD) of the resolved flow field is employed to obtain the coherent dynamics of the flow. To clearly demonstrate the oscillation characteristics and the horseshoe vortex structures of junction flow the velocity field in the plane of symmetry is decomposed with eduction of two dominant DMDmodes. These two DMDmodes are reconstituted and developed, together with the mean flow mode to explain the latent dynamics. Mode 1 reveals the merging of the horseshoe vortices and mode 2 is responsible for the process of fission and stretching.

The time-dependent mathematical model describing the vortex motion of an incompressible polymeric liquid is discussed. In the steady-state case certain particular solutions are found. In the case of the steady-state pressure along the axis of cylinder, a version of deriving this model for both fixed and free boundaries is given.

The steady flow arising in a spheroidal cavity with periodically-deformed elastic wall is studied experimentally. It is found that average flows whose intensities and structures depend on the wall oscillation frequency and amplitude can develop in the fluid. The average flow is generated in the Stokes boundary layer whose relative thickness is characterized by the dimensionless frequency of the vibrational action. Flow in the form of a pair of toroidal vortices which occupy the entire cavity volume can be observed over the range of low dimensionless frequencies when the boundary layer thickness is comparable with the characteristic cavity dimension. Increase in the dimensionless frequency (decrease in the relative thickness of the Stokes layers) leads to a displacement of the primary vortices towards the cavity boundary. In this case secondary vortices with opposite swirling are formed in the central part of the cavity above the primary vortices. The further increase in the dimensionless frequency leads to development of the secondary vortices and growth of the flow intensity. The large-scale secondary vortices occupy almost the entire cavity volume over the range of high dimensionless frequencies. The dependences of the regimes of average flows and their intensities on the control dimensionless parameters, the oscillation amplitude and frequency, are found on the basis of the results of the investigation.

Steady-state solutions to the problem of a thin vortex ring in an inviscid incompressible fluid in infinite space are investigated. The Fraenkel procedure is used to construct the steady-state solutions. In this procedure a given vorticity distribution in plane flow with circular streamlines is transformed into a steady vortex ring using an expansion in the ring thinness parameter. For example, a two-dimensional vortex of constant vorticity is transformed into a steady vortex ring with the uniform distribution in which the absolute value of vorticity is proportional to the distance from the axis of symmetry. The principal aim of our study is to construct the algorithm of finding the flow for an isochronous vortex ring in which the periods of revolution are the same for all the liquid particles in the vortex core. The problem is that the two-dimensional distribution which goes over in the isochronous ring in accordance with the Fraenkel procedure is unknown in advance. In particular, the ring with the uniform distribution is not isochronous despite the isochronism of the initial two-dimensional flow. In this connection the Fraenkel procedure is significantly modified so that the initial two-dimensional vorticity distribution is determined in each of the steps of the iteration procedure. The solution for the vortex ring with the uniform distribution obtained in the present study is significantly used to construct the isochronous solution. The necessary corrections to the former solution are calculated in each step. Obtaining of the isochronous flow is the key step for the investigation of stability of three-dimensional oscillations of the vortex ring since the oscillation spectrum of this flow is discrete.

The pattern of the two-dimensional vortex flow of a nonhomogeneous fluid in a confined domain is studied using two-dimensional numerical calculations. It is found that in the case of a nonhomogeneous initial density distribution the kinetic energy decay rates are proportional to the square root of viscosity at the active stage of flow restructuring. The correlation functions of the velocity and the density are derived for different moments of time in the inertial range. All these results indicate the choice of the two-dimensional turbulence development scenario in a nonhomogeneous fluid.

The solution of the Navier–Stokes equations which reproduces some qualitative features of localized turbulent structures developed in circular pipes at transitional Reynolds numbers is numerically investigated. In the phase space this solution corresponds to the limiting state of the solution which evolves along the separatrix dividing the regions of attraction of the solutions corresponding to the laminar and turbulent flow regimes. Relative simplicity of the spatial and temporal behavior of the limiting solution on the separatrix makes it possible to investigate it in detail. In particular, the nonlinear mechanism of the onset of streamwise vortices responsible for sustainment of near-wall streaks whose instability ensures the presence of fluctuations is revealed.

The results of visual investigations and direct numerical simulation of flow past a spanwise rib in a channel in a pulsating external flow at the Reynolds numbers corresponding to transition to turbulence in the separation region downstream of the rib in steady-state flow past the latter are represented. It is shown that the calculated and experimental data are in the adequate accordance. The effect of the forced unsteadiness parameters on the vortex flow structure downstream of the rib is analyzed. Some laws of the formation and evolution of the vortex structure downstream of the rib in a pulsating flow are obtained.

A regular system of vortex loops in annular flow behind the edge of a disk of 6–11 cm in diameter rotating in stratified fluid is first visualized using the shadowgraph techniques (classical method with the Foucault knife and the “filament-in-focus” method). Clearly outlined vortex loops are observed in strongly and weakly stratified fluids over a wide range of the angular disk rotation velocities. The dimensions of the vortex flow region depend on the stratification (buoyancy period), the angular velocity of rotation, and the disk diameter. Extended lengthy filaments which form spiral and irregular patterns inside the loops are clearly expressed in the fine flow structure. The filaments connect the neighboring loops. The trajectories of motion of the upper edges of the loops, i.e., the sources of short internal waves, are traced.

The effect of distributed blowing of a gas mass through a porous surface on the stability characteristics of a supersonic boundary layer is studied at a moderate supersonicMach numberM= 2. Tangential blowing when only the U-component of the mean velocity is not equal to zero on the wall is considered. The effect of the porous surface parameters on vortex perturbations is investigated and a comparison with the variant of the so-called “cutoff” regime is carried out. Different-density gas blowing is simulated by means of variation of the temperature factor (wall heating or cooling), namely, blowing of a heavy gas is simulated via blowing of a cold gas and vice versa.

The applicability of the criteria of existence of inviscid vortex structures (vortex Ferri singularities) is studied in the case in which a contact discontinuity of the corresponding intensity proceeds from the branching point of the λ shock wave configuration accompanying turbulent boundary layer separation under the action of an inner shock incident on the leeward wing panel. The calculated and experimental data are analyzed, in particular, those obtained using the special shadow technique developed for visualizing supersonic conical streams in nonsymmetric, Mach number 3 flow around a wing with zero sweep of the leading edges and the vee angle of 2π /3. The applicability of the criteria of existence of inviscid vortex structures is established for contact discontinuities generated by the λ shock wave configuration accompanying turbulent boundary layer separation realized under the action of a shock wave incident on the leeward wing panel. Thus, it is established that the formation of the vortex Ferri singularities in a shock layer is independent of the reason for the existence of the contact discontinuity and depends only on its intensity.

The motion of a buoyant vortex ring counter the direction of the lift of given value is experimentally investigated on a wide range of the initial velocity of the ring. The dynamics of its parameters are determined. The experimental results are compared with the calculations according to the earlier developed theoretical model. It is established in which cases the theoretical model describes the dynamics of buoyant vortex ring in motion counter the lift.

A vortex structure consisting of two concentric vortex rings located in a circular cylinder is studied. The rings touch each other and have a uniform vorticity. The geometric and dynamic parameters of the rings satisfy the condition of zero total intensity. A linear stability analysis of this structure is performed, including the limiting cases when the inner ring transforms into a circle or the outer ring is adjacent to the boundary of the cylinder. The results of numerical simulation of the evolution of unsteady flows are presented for a wide range of variation of governing parameters of the problem. It is established that the evolution of unstable vortex flows results in the formation of several types of quasistationary structures, the topology of which depends mainly on the dominant disturbance mode.